Abstract

We introduce a new concept called moment components and a new method based on it to obtain passive reduced-order models of interconnect networks. In this method, the impedance matrix moments of the interconnect network are partitioned into their inductive, capacitive and mixed inductive/capacitive moment components. The method of moment components is described in a formal manner using analysis and synthesis equalities. Two significant contributions of the method of moment components are: 1) new decomposition of moments into parts which reflect passivity in all moments of passive networks and 2) the analysis equalities impart a regular pattern in terms of the moment components, thus simplifying the moment generation for our method. None of these features is observable in conventional complete moment terms. Two new methods for obtaining passive reduced-order models based on the method of moment components are introduced. The passive reduced-order models are obtained by matching their impedance moment components to those of the original interconnect network through the synthesis equalities. Due to nonnegative definiteness of the moment components, the match in the moment components preserves the passivity of the original interconnect in the reduced-order model. The method of moment components does not have the instability problem of general moment matching techniques. The reduced-order model is specifically targeted for fast timing simulators so that interconnect effects can be simulated efficiently. Consequently, the calculation of all model parameters is based on explicitly formulated analytical expressions. To maintain the speed advantage of the fast timing simulator, the number of moments needs to be kept low. However, since the capacitive and inductive moment components of the original interconnect are matched respectively to the capacitive and inductive moment components of the reduced-order model, a more refined match is achieved and accurate results are obtained even with a small number of moments. Simulation results of original interconnect networks and their reduced-order models are compared using circuits of practical interest.